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THEONA—a numerical-analytical theory of motion of artificial satellites of celestial bodies

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Abstract

Basic principles of operation of the numerical-analytical theory THEONA (THéorie Numérique-Analytique) are presented, as well as force models taken into account and special functions used. Possibilities of applying the THEONA in problems of ballistic and navigation support are discussed. The accuracy of predicting the motion of the Earth’s satellites is estimated for various classes of orbits.

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References

  1. Bordovitsyna, T.V. and Avdyushev, V.A., Teoriya dvizheniya iskusstvennykh sputnikov Zemli. Analiticheskie i chislennye metody, (Theory of Motion of the Earth’s Satellites: Analytical and Numerical Methods), Tomsk: Izd-vo Tomskogo univ., 2007.

    Google Scholar 

  2. Fehlberg, Edwin, Some Old and New Runge-Kutta Formulas with Stepsize Control and Their Error Coefficients, Computing, vol.34, 1985, pp. 265–270.

    Article  MathSciNet  MATH  Google Scholar 

  3. Stepan’yants, V.A. and L’vov, D.V., An Efficient Algorithm for Solving Systems of Differential Equations of Motion, Mat. Model., 2000, vol. 12, no. 6, pp. 9–14.

    MATH  Google Scholar 

  4. Woodburn, James and Tanygin, Sergei, Efficient Numerical Integration of Coupled Orbit and Attitude Trajectories Using an Encke Type Correction Algorithm, AAS Paper 01-428, Advances in the Astronautical Sciences, Spaceflight Mechanics, 2001, vol. 109, pp. 1837–1848.

    Google Scholar 

  5. Lidov, M.L., Semi-Analytical Methods of Computing Satellite Motion, Trudy ITA AN SSSR, 1978, vol. 17, pp. 54–61.

    Google Scholar 

  6. Vashkov’yak, M.A., Method of Approximate Calculation of Motion of a Stationary Artificial Satellite of the Earth, Kosm. Issled., 1972, vol. 10, no. 2, pp. 147–158.

    ADS  Google Scholar 

  7. Vashkov’yak, M.A., On Numerical-Analytical Method for Calculating Motion of a 12-hour Satellite in Almost Circular Orbit, Kosm. Issled., 1983, vol. 21, no. 6, pp. 819–823.

    ADS  Google Scholar 

  8. Danielson, D.A., Sagovac, C.P., Neta, B., and Early, L.W., Semianalytic Satellite Theory (SST): Mathematical Algorithms, NPS-MA-95-002, Technical Report Naval Postgraduate School, Department of Mathematics, Monterey, CA, 1995.

  9. Yurasov, V.S., Application of Universal NumericalAnalytical Method for Prediction of Satellite Motion in the Atmosphere, in Nablyudeniya iskusstvennykh nebesnykh tel, (Observations of Artificial Celestial Bodies), Moscow: Astrosovet AN SSSR, 1984, no. 82.

    Google Scholar 

  10. Yurasov, V.S., Universal Semianalytic Satellite Motion Propagation Method, Proc. of the Second U.S.-Russian Second Space Surveillance Workshop, Poznan, Poland, July, 1996, pp. 198–211.

  11. Chazov, V.V., Calculation of Motion of Artificial Satellites in the Earth’s Gravitational Field, Nauchnye informatsii Astronomicheskogo soveta AN SSSR, 1987, vol.62, pp. 127–132.

    ADS  Google Scholar 

  12. Chazov, V.V., Basic Algorithms of Numerical-Analytical Theory of Motion of the Earth’s Satellites, Trudy Gos. Astronom. Inst. im. P.K. Shternberga, 2000, vol. 68, pp. 5–20.

    Google Scholar 

  13. Golikov, A.R., Numerical-Analytical Theory of Motion of Artificial Satellites of Celestial Bodies, Preprint of Keldysh Inst. of Applied Math., Russ. Acad. Sci., Moscow,, 1990, no. 70.

  14. Golikov, A.R., Effect of Noncentrality of Gravitational Field in Numerical-Analytical Theory of Motion of Artificial Satellites, Preprint of Keldysh Inst. of Applied Math., Russ. Acad. Sci., Moscow,, 1991 no. 49.

  15. Golikov, A.R., Influence of Atmospheric Drag in Numerical-Analytical Theory of Motion of the Earth’s Satellites, Preprint of Keldysh Inst. of Applied Math., Russ. Acad. Sci., Moscow, 1991 no. 65.

  16. Akim, E.L. and Golikov, A.R., Numeric-Analytical Satellite Theory, Paper no. AAS 93-315 in Advances in the Astronomical Sciences, 8th Intern. Symp. On Space Flight Dynamics, Greenbelt, USA, April 1993.

  17. Akim, E.L. and Golikov, A.R., NA-Theory: The Precise Method for Prediction of the Satellite Motion in the Earth Atmosphere, Proc. of the 9th Intern. Symp. on Space Flight Dynamics, St.Petersburg-Moscow, Russia, May1994.

  18. Golikov, A.R., Numerical-Analytical Theory THEONA and Analysis of Motion of Satellite Systems, Trudy MAI, 2009, no. 34.

  19. Baranov, A. and Golikov, A., Optimal Maneuvers for Station Keeping for a Given Configuration of the Satellite Constellation, Journal of the Brazilian Society of Mechanical Sciences, 14th Intern. Symp. On Space Flight Dynamics, Foz do Iguaçu, Brazil, February 1999, pp. 482–486.

  20. Golikov, A.R., Evolution of Formation Flying Satellite Relative Motion: Analysis Based on the THEONA Satellite Theory, Proc. of the 17th Intern. Symp. On Spacec Flight Dynamics, Moscow, Russia, June, 2003.

  21. Golikov, A., THEONA Theory of Relative Satellite Motion Flying in the Formation, Proc. of 18th Intern. Symp. On Space Flight Dynamics, Munich, Germany, October 2004, pp. 59–66.

  22. Golikov, A.R., New Approach in Dynamics Problems of Earth Satellite Formations Flying, Actual Problems of Aviation and Aerospace Systems: processes, models, experiment (APAAS), KAI-KSTU (Kazan-Daytona Beach), 2007, vol. 12,issue 1(23).

  23. Akim, E. and Golikov, A., On Determination of the Parameters of Gravitational Field Using the Numeric-Analytical Satellite Theory, Proc. of the 10th Intern. Symp. On Space Flight Dynamics, Toulouse, France, June 1995, paper no. MS 95/045..

  24. Akim, E. and Golikov, A., Combined Model of the Lunar Gravity Field, Proc. of the 12th Intern. Symp. on Space Flight Dynamics Held 2–6 June 1997 in Darmstadt, Germany, ESA SP-403, Paris: European Space Agency, 1997, p. 357.

    Google Scholar 

  25. Aksenov, E.P., Grebenikov, E.A., and Demin, V.G., General Solution to the Problem of Motion of an Artificial Satellite in Normal Field of the Earth’s Attraction, Iskusstvennye Sputniki Zemli, 1961, no. 8, p. 64.

  26. Aksenov, E.P., Grebenikov, E.A., and Demin, V.G., Generalized Problem of Two Fixed Centers and Its Application in the Theory of Motion of Earth Artificial Satellites, Astron. Zh., 1963, vol. 40, no. 2, pp. 363–372.

    MathSciNet  ADS  MATH  Google Scholar 

  27. Demin, V.G., Dvizhenie iskusstvennogo sputnika v netsentral’nom pole tyagoteniya Zemli (Motion of an Artificial Satellite in the Noncentral Field of Earth’s Gravity), Moscow: Nauka, 1968.

    Google Scholar 

  28. Aksenov, E.P., Teoriya dvizheniya iskusstvennykh sputnikov Zemli (Theory of Motion of Earth’s Artificial Satellites), Moscow: Nauka, 1977, p. 360.

    Google Scholar 

  29. Lukyanov, L.G., Emeljanov, N.V., and Shirmin, G.I., Generalized Problem of Two Fixed Centers or the Darboux-Gredeaks Problem, Kosm. Issled., 2005, vol. 43, no. 3, pp. 194–200. [Cosmic Research, pp. 186–191].

    Google Scholar 

  30. Akim, E.L. and Vlasova, Z.P., Model of Gravitational Field of the Moon Deduced from Observations of Its Artificial Satellites Luna-10,12,14,19, and 22, Dokl. Akad. Nauk SSSR, 1977, vol. 235, no. 1.

  31. Akim, E.L., Determination of Astronomical Constants Using Measurements of Spacecraft Trajectories of Motion, Doctoral (Phys.-Math.) Dissertation, Moscow: Keldysh Inst. of Applied Math., 1981.

    Google Scholar 

  32. Akim, E.L., Pochukaev, V.N., and Pavlov, V.N., Pole tyagoteniya Luny i dvizhenie ee iskusstvennykh sputnikov (Gravity Field of the Moon and Motion of Its Artificial Satellites), Moscow: Nauka, 1984.

    Google Scholar 

  33. GOST (State Standard) 22721-77: Model of the Upper Atmosphere for Ballistic Calculations, 1978.

  34. GOST (State Standard) 25645.115-84: The Earth’s Upper Atmosphere. A Model of Density for Navigation Support of Flights of the Earth’s Artificial Satellites, 1991 (Wording of 1990).

  35. GOST (State Standard) R 25645.000-2001: The Earth’s Upper Atmosphere. A Model of Density for Navigation Support of Flights of the Earth’s Artificial Satellites, 2002.

  36. GOST (State Standard) R 25645.166-2004: The Earth’s Upper Atmosphere. A Model of Density for Navigation Support of Flights of the Earth’s Artificial Satellites, 2004.

  37. Picone, J.M., Hedin, A.E., Drob, D.P., and Aikin, A.C., NRL-MSISE-00 Empirical Model of the Atmosphere: Statistical Comparisons and Scientific Issues, J. Geophys. Res., 2002, vol. 107, pp. 1468–1483. doi: 10. 1029/2002JA009430.

    Article  Google Scholar 

  38. Bruinsma, S., Thuillier, G., and Barlier, F., The DTM-2000 Empirical Thermosphere Model with New Data Assimilation and Constraints at Lower Boundary: Accuracy and Properties, J. of Atm. and Solar-Terr. Physics, 2003, vol. 65, pp. 1053–1070. doi: 10.1016/S1364-6826(03)00137-8.

    Article  ADS  Google Scholar 

  39. Sehnal, L. and Pospišilová, L., Thermospheric Model TD 88, Preprint of Astronomical Institute, Czechoslovak Academy of Sciences, Observatory Ondrejov, 1988, no. 67.

  40. Šurlan, B. and Šegan, S., TD-88Up—Upgraded Neutral Earth’s Thermosphere Total Density TD-88 Model, Serbian Astronomical Journal, 2009, vol. 178, pp. 57–63.

    ADS  Google Scholar 

  41. Justh, H.L., Justus, C.G., and Ramey, H.S., The Next Generation of Mars-GRAM and Its Role in the Autonomous Aerobraking Development Plan, Paper AAS 11-478 in Advances in the Astronautical Sciences, 2011.

  42. The Venus International Reference Atmosphere, Kliore, A.J., Moroz, V.I., and Keating, G.M., Eds., Advances in Space Research, 1985, vol. 5, no. 11, pp. 1–304.

  43. Justh, H.L., Justus, C.G., and Keller, V.W., Global Reference Atmospheric Models, Including Thermospheres, for Mars, Venus and Earth, Paper AIAA-2006-6394, AIAA/AAS Astrodynamics Specialist Conference & Exhibit., 21–24 August, 2006, Keystone, CO.

  44. Standish, E.M., JPL Planetary and Lunar ephemerides, DE405/LE405, JPL Interoffice Memorandum IOM 312.F-98-048, Aug. 26, 1998.

  45. Folkner, W.M., Standish, E.M., Williams, J.G., and Boggs, D.H., Planetary and Lunar Ephemeris DE418, JPL Interoffice Memorandum IOM 343.R-07-005, Aug. 2, 2007.

  46. Vilenkin, N.Ya., Spetsial’nye funktsii i teoriya predstavlenii grupp (Special Functions and Group Representation Theory), Moscow: Nauka, 1965.

    Google Scholar 

  47. Golikov, A.R., Semi-Analytical Theory THEONA & Its Special Functions, 4th Intern. Workshop and Advanced School “Spaceflight Dynamics and Control,” Covilha, Portugal, October 2008.

  48. Marsh, J.G. and Williamson, R.G., Precision Orbit Computations for Starlette, Journal of Geodesy, 1978, vol. 52, no. 1, pp. 71–83.

    Google Scholar 

  49. Bertotti, B., Farinella, P., and Vokrouhlický, D., Physics of the Solar System: Dynamics and Evolution, Space Physics, and Spacetime Structure, Kluwer Academic Springer, 2003, p. 606, Table 18.1.

  50. Damaren, C.J., Spacecraft Formation Flying, Univ. of Toronto Inst. for Aerospace Studies, Presented to U of T Space Design Contest Participants, December 2009.

  51. Baranov, A.A. and Baranov, A.A., Maintenance of a Preset Configuration of Satellite Constellation, Kosm. Issled., 2009, vol. 47, no. 1, pp. 48–54. (Only in Russian).

    Google Scholar 

  52. Baranov, A.A. and Baranov, A.A., Algorithms for Calculating Parameters of Maneuvers of Satellite System Formation, Kosm. Issled., 2009, vol. 47, no. 3, pp. 1–7. (Only in Russian).

    MathSciNet  Google Scholar 

  53. Baranov, A.A., de Prado, A.F.B., Razumny V.Yu., and Baranov, A.A., Jr., Optimal Low-Thrust Transfers between Close Near-Circular Coplanar Orbits, Kosm. Issled., 2011, vol. 49, no. 3, pp. 278–288. [Cosmic Research, pp. 269–279].

    Google Scholar 

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Correspondence to A. R. Golikov.

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Original Russian Text © A.R. Golikov, 2012, published in Kosmicheskie Issledovaniya, 2012, Vol. 50, No. 6, pp. 480–489.

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Golikov, A.R. THEONA—a numerical-analytical theory of motion of artificial satellites of celestial bodies. Cosmic Res 50, 449–458 (2012). https://doi.org/10.1134/S0010952512060020

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